上海交通大学学报 ›› 2026, Vol. 60 ›› Issue (8): 1299-1311.doi: 10.16183/j.cnki.jsjtu.2025.227
李洪森a,b,c,d, 张朋b,c,d(
), 王明a,b,c,d, 张洁b,c,d, 相文彬b,c,d,e
收稿日期:2025-07-10
修回日期:2025-10-22
接受日期:2025-11-24
出版日期:2026-08-28
发布日期:2026-09-02
通讯作者:
张 朋,副教授;E-mail:zhangp88@dhu.edu.cn.
作者简介:李洪森(2001—),硕士生,从事机器人调度研究.
基金资助:
LI Hongsena,b,c,d, ZHANG Pengb,c,d(
), WANG Minga,b,c,d, ZHANG Jieb,c,d, XIANG Wenbinb,c,d,e
Received:2025-07-10
Revised:2025-10-22
Accepted:2025-11-24
Online:2026-08-28
Published:2026-09-02
摘要:
针对带设备预防性维护的焊接流水车间调度问题,以最大完工时间最小化为优化目标,考虑设备故障冲击、有限缓冲区及高维状态空间导致表征模糊等难点,提出基于表征增强多智能体强化学习的调度与维护联合优化方法.将问题拆分为加工调度和预防性维护两个子问题,构建调度-维护双智能体架构;子问题存在强耦合性,其中调度会影响设备故障风险,维护会改变设备可用状态,而双智能体通过价值分解多智能体演员-评论家(VDAC)算法将全局价值函数分解为双智能体的局部价值函数,使两者在优化各自局部价值时自然嵌入对于对方子问题的考量,从而实现协同求解;表征增强通过自编码器提炼高维状态的关键信息,解决了高维状态空间信息冗余、表征模糊问题,使智能体能基于关键表征信息决策,提升调度与维护联合优化性能.算例验证显示,最小化的最大完工时间较其他算法平均减少4.13%,较规则算法平均减少13.34%.
中图分类号:
李洪森, 张朋, 王明, 张洁, 相文彬. 基于表征增强多智能体强化学习的焊接流水车间调度与维护联合优化方法[J]. 上海交通大学学报, 2026, 60(8): 1299-1311.
LI Hongsen, ZHANG Peng, WANG Ming, ZHANG Jie, XIANG Wenbin. Integrated Optimization Method for Scheduling and Maintenance in Welding Flow Shops Based on Representation-Enhanced Multi-Agent Reinforcement Learning[J]. Journal of Shanghai Jiao Tong University, 2026, 60(8): 1299-1311.
表1
符号定义
| 符号 | 定义 |
|---|---|
| Ai | 工作站i机器维护后的初始寿命 |
| Ai(t) | 时间t工作站i机器的役龄 |
| bi(t) | 第i个缓冲区在时间t的工件数 |
| Bi | 第i个缓冲区的缓冲容量 |
| Rthd | 机器的可靠度阈值 |
| Oj,k | 工件j的第k道工序 |
| 机器集合,索引i=1, 2, …, n | |
| Ri(t) | 工作站i机器在时间t的可靠度 |
| T | 预防性维护时间 |
| Tc | 纠错性维护时间 |
| 加工的当前时间 | |
| Tmi | 工作站i中机器加工的结束时间 |
| 工作站i的机器第j次预防性维护的开始时间 | |
| TEi,j,k | 工作站i、加工工件j的第k道工序的完成时间 |
| TPi,j,k | 工作站i、加工工件j的第k道工序的加工时间 |
| TSi,j,k | 工作站i、加工工件j的第k道工序的开始时间 |
| Wi | 工作站集合,索引i=1, 2, …, n |
| Xi,j,k | 表示工件j的第k个工序在工作站i中的机器加工为1,否则为0 |
| θi(t) | 工作站i机器在时间t的状态 |
表5
不同算法的最大完工时间对比
| 案例 规模 | AE-VDAC | MAPPO | DQN | QPLEX | FACMAC | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 均值/ h | 最小 值/h | 最大 值/h | 均值/ h | 最小 值/h | 最大 值/h | 均值/ h | 最小 值/h | 最大 值/h | 均值/ h | 最小 值/h | 最大 值/h | 均值/ h | 最小 值/h | 最大 值/h | |||||||
| 6×6 | 71.5 | 71.0 | 72.0 | 70.0 | 70.0 | 70.0 | 70.0 | 70.0 | 70.0 | 70.4 | 70.0 | 71.0 | 71.0 | 70.0 | 72.0 | ||||||
| 10×6 | 112.6 | 110.0 | 116.0 | 110.6 | 110.0 | 113.0 | 110.2 | 110.0 | 112.0 | 113.2 | 112.0 | 116.0 | 109.0 | 108.0 | 110.0 | ||||||
| 15×6 | 156.0 | 154.0 | 157.0 | 160.5 | 160.0 | 161.0 | 160.2 | 157.0 | 162.0 | 159.8 | 158.0 | 161.0 | 157.4 | 155.0 | 159.0 | ||||||
| 20×6 | 206.2 | 202.0 | 213.0 | 207.0 | 198.0 | 218.0 | 208.4 | 203.0 | 216.0 | 205.6 | 201.0 | 213.0 | 208.2 | 203.0 | 215.0 | ||||||
| 25×6 | 246.5 | 242.0 | 258.0 | 261.6 | 256.0 | 266.0 | 257.8 | 254.0 | 260.0 | 251.2 | 244.0 | 259.0 | 253.3 | 245.0 | 265.0 | ||||||
| 30×6 | 300.0 | 296.0 | 303.0 | 311.2 | 306.0 | 315.0 | 304.4 | 300.0 | 312.0 | 303.0 | 299.0 | 306.0 | 308.3 | 302.0 | 317.0 | ||||||
| 35×6 | 321.2 | 321.0 | 322.0 | 352.2 | 346.0 | 357.0 | 357.3 | 354.0 | 362.0 | 332.4 | 326.0 | 342.0 | 337.6 | 328.0 | 346.0 | ||||||
| 40×6 | 390.3 | 387.0 | 394.0 | 398.8 | 390.0 | 408.0 | 398.4 | 389.0 | 415.0 | 400.6 | 396.0 | 408.0 | 397.7 | 394.0 | 404.0 | ||||||
| 45×6 | 434.2 | 429.0 | 438.0 | 455.8 | 450.0 | 462.0 | 456.8 | 455.0 | 460.0 | 445.0 | 441.0 | 450.0 | 454.4 | 451.0 | 458.0 | ||||||
| 50×6 | 477.8 | 476.0 | 480.0 | 512.3 | 502.0 | 527.0 | 495.9 | 493.0 | 500.0 | 484.3 | 479.0 | 488.0 | 487.3 | 480.0 | 491.0 | ||||||
| 6×8 | 90.2 | 89.0 | 92.0 | 87.7 | 86.0 | 89.0 | 90.0 | 90.0 | 90.0 | 87.0 | 86.0 | 88.0 | 87.4 | 86.0 | 89.0 | ||||||
| 10×8 | 122.2 | 122.0 | 124.0 | 126.0 | 125.0 | 129.0 | 127.6 | 127.0 | 129.0 | 124.2 | 123.0 | 126.0 | 121.0 | 120.0 | 123.0 | ||||||
| 15×8 | 157.4 | 157.0 | 158.0 | 169.2 | 169.0 | 170.0 | 167.2 | 164.0 | 171.0 | 159.6 | 158.0 | 161.0 | 163.0 | 162.0 | 164.0 | ||||||
| 20×8 | 208.3 | 206.0 | 214.0 | 219.0 | 211.0 | 226.0 | 210.7 | 207.0 | 214.0 | 210.6 | 207.0 | 216.0 | 211.8 | 208.0 | 216.0 | ||||||
| 25×8 | 254.4 | 251.0 | 260.0 | 265.8 | 262.0 | 270.0 | 268.8 | 268.0 | 270.0 | 265.5 | 258.0 | 276.0 | 262.8 | 260.0 | 265.0 | ||||||
| 30×8 | 303.2 | 299.0 | 308.0 | 316.7 | 314.0 | 324.0 | 315.7 | 312.0 | 323.0 | 309.0 | 302.0 | 316.0 | 309.4 | 304.0 | 314.0 | ||||||
| 35×8 | 331.1 | 331.0 | 332.0 | 369.6 | 361.0 | 374.0 | 373.8 | 370.0 | 375.0 | 358.6 | 355.0 | 362.0 | 352.0 | 349.0 | 357.0 | ||||||
| 40×8 | 392.5 | 388.0 | 402.0 | 433.6 | 424.0 | 437.0 | 435.0 | 430.0 | 441.0 | 417.0 | 411.0 | 425.0 | 421.2 | 415.0 | 426.0 | ||||||
| 45×8 | 439.2 | 436.0 | 444.0 | 484.2 | 481.0 | 490.0 | 484.3 | 483.0 | 485.0 | 451.8 | 448.0 | 456.0 | 454.6 | 452.0 | 459.0 | ||||||
| 50×8 | 487.8 | 485.0 | 490.0 | 521.5 | 514.0 | 530.0 | 512.5 | 510.0 | 516.0 | 504.7 | 493.0 | 510.0 | 505.2 | 493.0 | 512.0 | ||||||
表6
与柔性预防性维护规则算法的最大完工时间对比
| 案例 规模 | AE-VDAC最大完工时间/h | 最大完工时间/h | ||||||
|---|---|---|---|---|---|---|---|---|
| 均值 | 最小值 | 最大值 | SPT | LPT | MWKR | FIFO | ||
| 6×6 | 71.5 | 71.0 | 72.0 | 76.0 | 85.0 | 104.0 | 88.0 | |
| 10×6 | 112.6 | 110.0 | 116.0 | 115.0 | 135.0 | 119.0 | 126.0 | |
| 15×6 | 156.0 | 154.0 | 157.0 | 179.0 | 202.0 | 201.0 | 192.0 | |
| 20×6 | 206.2 | 202.0 | 213.0 | 217.0 | 243.0 | 242.0 | 225.0 | |
| 25×6 | 246.5 | 242.0 | 258.0 | 265.0 | 302.0 | 297.0 | 276.0 | |
| 30×6 | 300.0 | 296.0 | 303.0 | 323.0 | 360.0 | 357.0 | 317.0 | |
| 35×6 | 321.2 | 321.0 | 322.0 | 362.0 | 395.0 | 399.0 | 359.0 | |
| 40×6 | 390.3 | 387.0 | 394.0 | 437.0 | 465.0 | 463.0 | 415.0 | |
| 45×6 | 434.2 | 429.0 | 438.0 | 498.0 | 528.0 | 526.0 | 490.0 | |
| 50×6 | 477.8 | 476.0 | 480.0 | 516.0 | 556.0 | 538.0 | 513.0 | |
| 6×8 | 90.2 | 89.0 | 92.0 | 97.0 | 100.0 | 107.0 | 102.0 | |
| 10×8 | 122.2 | 122.0 | 124.0 | 129.0 | 154.0 | 130.0 | 138.0 | |
| 15×8 | 157.4 | 157.0 | 158.0 | 178.0 | 195.0 | 172.0 | 181.0 | |
| 20×8 | 208.3 | 206.0 | 214.0 | 223.0 | 239.0 | 227.0 | 230.0 | |
| 25×8 | 254.4 | 251.0 | 260.0 | 283.0 | 288.0 | 272.0 | 282.0 | |
| 30×8 | 303.2 | 299.0 | 308.0 | 320.0 | 338.0 | 319.0 | 320.0 | |
| 35×8 | 331.2 | 331.0 | 332.0 | 371.0 | 394.0 | 386.0 | 381.0 | |
| 40×8 | 392.5 | 388.0 | 402.0 | 438.0 | 457.0 | 442.0 | 438.0 | |
| 45×8 | 439.2 | 436.0 | 444.0 | 490.0 | 502.0 | 492.0 | 498.0 | |
| 50×8 | 487.8 | 485.0 | 490.0 | 533.0 | 553.0 | 529.0 | 525.0 | |
表7
不同表征增强方法最大完工时间对比
| 案例 规模 | AE-VDAC | PCA-VDAC | VAE-VDAC | RND-VDAC | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 均值/h | 最小 值/h | 最大 值/h | 均值/h | 最小 值/h | 最大 值/h | 均值/h | 最小 值/h | 最大 值/h | 均值/h | 最小 值/h | 最大 值/h | ||||
| 6×8 | 90.2 | 89.0 | 92.0 | 95.5 | 94.0 | 98.0 | 97.0 | 95.0 | 101.0 | 99.6 | 95.0 | 105.0 | |||
| 10×8 | 122.2 | 122.0 | 124.0 | 124.3 | 122.0 | 127.0 | 136.3 | 133.0 | 141.0 | 138.0 | 133.0 | 143.0 | |||
| 15×8 | 157.4 | 157.0 | 158.0 | 171.4 | 167.0 | 176.0 | 188.6 | 183.0 | 194.0 | 170.3 | 166.0 | 174.0 | |||
| 20×8 | 208.3 | 206.0 | 214.0 | 218.2 | 215.0 | 222.0 | 218.2 | 210.0 | 225.0 | 226.8 | 214.0 | 232.0 | |||
| 25×8 | 254.4 | 251.0 | 260.0 | 263.4 | 255.0 | 271.0 | 293.6 | 281.0 | 306.0 | 294.2 | 286.0 | 305.0 | |||
| 30×8 | 303.2 | 299.0 | 308.0 | 323.6 | 319.0 | 327.0 | 351.4 | 344.0 | 371.0 | 352.2 | 342.0 | 366.0 | |||
| 35×8 | 331.2 | 331.0 | 332.0 | 366.0 | 363.0 | 368.0 | 392.0 | 377.0 | 403.0 | 398.2 | 390.0 | 415.0 | |||
| 40×8 | 392.5 | 388.0 | 402.0 | 408.6 | 405.0 | 415.0 | 435.0 | 430.0 | 441.0 | 464.2 | 456.0 | 478.0 | |||
| 45×8 | 439.2 | 436.0 | 444.0 | 453.3 | 449.0 | 457.0 | 503.0 | 489.0 | 513.0 | 512.0 | 505.0 | 521.0 | |||
| 50×8 | 487.8 | 485.0 | 490.0 | 497.0 | 492.0 | 500.0 | 541.6 | 530.0 | 550.0 | 559.3 | 545.0 | 567.0 | |||
表8
工件各个阶段加工时间
| 工件 编号 | 加工时间/h | 工件 编号 | 加工时间/h | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 小部件 拼接 | 大部件 拼接 | 内缝 拼接 | 箱盖 封装 | 外缝 焊接 | 小部件 拼接 | 大部件 拼接 | 内缝 拼接 | 箱盖 封装 | 外缝 焊接 | ||
| 1 | 8 | 2 | 6 | 7 | 9 | 19 | 4 | 6 | 3 | 3 | 7 |
| 2 | 4 | 6 | 7 | 8 | 2 | 20 | 4 | 6 | 2 | 4 | 2 |
| 3 | 4 | 6 | 8 | 3 | 7 | 21 | 5 | 4 | 8 | 9 | 1 |
| 4 | 5 | 2 | 7 | 8 | 1 | 22 | 5 | 4 | 5 | 3 | 8 |
| 5 | 5 | 4 | 8 | 9 | 1 | 23 | 2 | 3 | 9 | 6 | 1 |
| 6 | 5 | 5 | 5 | 3 | 8 | 24 | 4 | 6 | 8 | 3 | 7 |
| 7 | 2 | 3 | 9 | 6 | 1 | 25 | 5 | 2 | 7 | 8 | 1 |
| 8 | 5 | 4 | 8 | 9 | 1 | 26 | 8 | 2 | 6 | 7 | 9 |
| 9 | 4 | 6 | 8 | 3 | 7 | 27 | 5 | 4 | 8 | 9 | 1 |
| 10 | 6 | 6 | 2 | 4 | 3 | 28 | 5 | 5 | 5 | 3 | 8 |
| 11 | 6 | 5 | 1 | 9 | 2 | 29 | 6 | 5 | 1 | 9 | 2 |
| 12 | 2 | 3 | 9 | 6 | 1 | 30 | 8 | 2 | 6 | 7 | 9 |
| 13 | 9 | 3 | 5 | 4 | 6 | 31 | 7 | 2 | 6 | 8 | 9 |
| 14 | 5 | 6 | 7 | 4 | 1 | 32 | 6 | 5 | 3 | 9 | 2 |
| 15 | 5 | 2 | 7 | 8 | 1 | 33 | 5 | 8 | 7 | 8 | 7 |
| 16 | 5 | 5 | 5 | 3 | 8 | 34 | 7 | 5 | 8 | 5 | 10 |
| 17 | 6 | 3 | 9 | 6 | 5 | 35 | 5 | 5 | 8 | 6 | 2 |
| 18 | 5 | 8 | 8 | 9 | 1 | ||||||
表9
企业实例不同算法的最大完工时间对比
| 案例 规模 | AE-VDAC | MAPPO | DQN | QPLEX | FACMAC | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 均值/ h | 最小 值/h | 最大 值/h | 均值/ h | 最小 值/h | 最大 值/h | 均值/ h | 最小 值/h | 最大 值/h | 均值/ h | 最小 值/h | 最大 值/h | 均值/ h | 最小 值/h | 最大 值/h | |||||||
| 15×5 | 122.2 | 121.0 | 125.0 | 126.2 | 124.0 | 128.0 | 123.4 | 122.0 | 126.0 | 123.4 | 122.0 | 128.0 | 123.2 | 122.0 | 126.0 | ||||||
| 20×5 | 159.4 | 158.0 | 161.0 | 163.0 | 160.0 | 164.0 | 165.8 | 162.0 | 170.0 | 163.8 | 159.0 | 172.0 | 161.5 | 157.0 | 165.0 | ||||||
| 25×5 | 205.8 | 202.0 | 210.0 | 209.0 | 205.0 | 214.0 | 211.8 | 207.0 | 216.0 | 209.0 | 204.0 | 215.0 | 211.6 | 205.0 | 217.0 | ||||||
| 30×5 | 247.6 | 242.0 | 254.0 | 255.5 | 252.0 | 263.0 | 257.8 | 252.0 | 267.0 | 252.0 | 247.0 | 255.0 | 255.0 | 250.0 | 257.0 | ||||||
| 35×5 | 287.4 | 285.0 | 290.0 | 297.8 | 294.0 | 300.0 | 300.5 | 296.0 | 305.0 | 298.5 | 295.0 | 301.0 | 299.0 | 294.0 | 305.0 | ||||||
表10
企业实例中与柔性预防性维护规则算法的最大完工时间对比
| 案例 规模 | AE-VDAC最大完工时间/h | 最大完工时间/h | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 均值 | 最小值 | 最大值 | SPT | LPT | MWKR | FIFO | |||||
| 15×5 | 122.2 | 121.0 | 125.0 | 129.0 | 148.0 | 135.0 | 148.0 | ||||
| 20×5 | 159.4 | 158.0 | 161.0 | 174.0 | 183.0 | 178.0 | 177.0 | ||||
| 25×5 | 205.8 | 202.0 | 210.0 | 218.0 | 224.0 | 225.0 | 221.0 | ||||
| 30×5 | 247.6 | 242.0 | 254.0 | 267.0 | 276.0 | 277.0 | 272.0 | ||||
| 35×5 | 287.4 | 285.0 | 290.0 | 310.0 | 316.0 | 314.0 | 314.0 | ||||
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